BS 3rd Physical Chemistry Midterm PDF

Thermodynamics Thermodynamics is a branch of physics and Chemistry that deals with the relationship between heat, work, and energy. It is a fundamental-science that is use understand-a-wide-range of physical phenomena, from the behavior of to the workings of engines. At its core, thermodynamics is c...

Thermodynamics Thermodynamics is a branch of physics and Chemistry that deals with the relationship between heat, work, and energy. It is a fundamental-science that is use understand-a-wide-range of physical phenomena, from the behavior of to the workings of engines. At its core, thermodynamics is concerned w energy-is-transferred and transformed within-physical-systems. System One of the key concepts in thermodynamics is the idea of a system. A system is simply a portion of the universe that is being studied. It can be anything- from a simple gas in a container to a complex biological organism. The behavior of a system is determined by its thermodynamic properties, which include temperature, pressure, volume, and energy.¶ Equation of State In-physics and thermodynamics, an equation of state is a mathematic relationship that describes the behavior of a physical system in terms thermodynamic properties, such as pressure, volume, and temperature mathematical-description allows scientists and engineers to predict a analyze the behavior of a system, and has applications in a variety of from-chemistry-and-materials science to aerospace engineering and e production. Understanding the concept of equation of state In order to understand equations of state, it is important to first grasp t underlying principles of thermodynamics. The study of thermodynamic concerned-with-how-energy is transferred and transformed within systems, and equations of state are a fundamental tool in this field, se a means of relating macroscopic properties to the behavior of individual molecules. Importance in thermodynamics Equations of state play a fundamental role in predicting and understanding the behavior of matter over a wide range of conditions. By providing a mathematical description of the relationship between thermodynamic properties, equations of state allow researchers to study a wide variety of physical phenomena, from phase transitions to chemical reactions.¶ Types of equations of state¶ Equations of state are mathematical expressions that relate the physical properties of a substance, such as pressure, volume, and temperature, to each other. There are several different types of equations of state that are commonly used in a variety of applications. Each equation has its own unique strengths and limitations, and may be more or less appropriate depending on the physical system being studied.¶ Ideal gas law One of the most fundamental equations of state is the ideal gas law, which describes the behavior of gases at low pressure and high temperature. The ideal gas law relates the pressure, volume, and temperature of a gas sample and is often used to make approximations in a wide range of applications, from atmospheric science to engineering. 𝑃𝑉 = 𝑛𝑅𝑇 For example, the ideal gas-law can be used to estimate the volume of a gas at a given temperature and pressure, or to calculate the pressure of a gas at a given volume and temperature. It is also used in the design of engines and other machinery that involve the compression and expansion of gases.¶ Van-der-Waals equation The Van der Waals equation is a modification of the ideal gas law that accounts for the attractive and repulsive forces between gas molecules. This equation is commonly used to describe the behavior of gases at moderate pressures and temperatures, and provides a more accurate description than the ideal gas law in many scenarios.¶ 𝑎𝑛2 [𝑃 + 2 ] × [𝑉 − 𝑛𝑏] = 𝑛𝑅𝑇 𝑉 The Van der Waals equation takes into account the volume of the gas molecules themselves, as well as the attractive forces between them. This makes it more accurate than the ideal gas law in situations where the gas molecules are relatively close together and interact with each other.¶ Virial equation of state¶ The virial equation of state is basically a power series of the concentration (1/Vm ). B(T), C(T) and D(T) are the second, third and fourth virial coefficients. Substituting V/n for Vm we have The Virial equation of state is a more complex equation that can be used to describe the behavior of gases and liquids over a wider range of pressures and temperatures. The Virial equation accounts not only for the pairwise interactions of gas molecules, but also considers the interactions between three or more molecules, making it a more accurate description for complex systems. Applications of equations of state¶ Equations of state-are-used in a wide range of applications, from chemistry and materials science to aerospace engineering and energy. production designing. engines and turbines to developing new materials and drugs. They are an essential tool in the study of thermodynamics and are used by researchers around the world to better understand the behavior of matter under different conditions. Predicting phase behavior One of the most important applications of equations of state is in predicting the phase behavior of a system. Researchers can use equations of state. along with other thermodynamic models to predict how a substance will behave under various conditions, such as temperature, pressure, and composition. Understanding the phase behavior of a system is critical for may industrial processes, such as chemical separation and distillation.¶ Calculating thermodynamic properties Equations of state can also be used to calculate a wide range of thermodynamic properties, such as entropy, enthalpy, and fugacity. These properties can be used to predict how a system will behave under different conditions, and can help scientists and engineers design and optimize a wide variety of processes.¶ Modeling chemical reactions Equations of state are a crucial tool in modeling and simulating chemical. reactions, allowing researchers to predict how reactants will behave under different conditions. These models are important for many fields, such as pharmaceuticals, where researchers use them to model drug reactions and optimize drug-design.¶ pharmaceuticals, where researchers use them to model drug reactions and optimize drug design.¶ Engineering and industrial applications Equations of state are also used extensively in many engineering and- industrial applications, from designing chemical reactors to developing new- materials for energy storage. By providing a mathematical description of the behavior of a system, equations of state allow engineers to design- and- optimize processes while minimizing costs and maximizing efficiency. Ideal and Real Gases Gas is a funny type of matter. Unlike solids or liquids, gases don't have a fixed volume and instead take the shape of whatever container they're in. But did you know that not all gases behave the same way? That's where ideal gases come in. Ideal gases are theoretical gases that behave exactly as predicted under all conditions. This makes it easier to study gases and figure out how they work. The Ideal Gas Law is a formula that explains the behavior of ideal gases. It says that for an ideal gas, pressure times volume is always equal to the number of gas molecules times a constant (called the Gas Constant) times temperature. All gases that exist in the environment are Real Gases, and they follow the Ideal Gas Law only under certain conditions. While ideal gas is a hypothetical gas that follows the Ideal Gas Law at all conditions of temperature and pressure, real gases only behave like ideal gases under conditions of high temperature and low pressure. When it comes to describing gases, the Ideal Gas Law is just one of many equations used to explain how gases behave. So, next time you're studying gases, remember that ideal and real gases are two different things, and there's a lot to learn about how gases behave. Properties of Ideal and Real Gases Ideal Gas and Real Gas: How Are They Different? Ideal gases are theoretical gases that follow gas laws at all temperatures and pressures. They are made up of solid, spherical particles that don't attract or repel each other. The motion of the gas molecules is completely random, and they travel in a straight line until they hit another particle or the container wall. The collision of these particles with each other or the wall is completely elastic, which means the kinetic energy of the gas remains constant. However, any gas that exists in reality is a real gas. Real gases can never be perfectly ideal because atoms and molecules will always have some forces of attraction or repulsion between them, and they occupy some volume. Under some conditions, the size of atoms or molecules can no longer be considered negligible as compared to the distance between the particles. Generally, gases behave more like ideal gases at high temperatures and low pressures, while they deviate from ideal gas behavior at low temperatures or high pressures. At standard temperature and pressure, some gases such as Hydrogen, Oxygen, Nitrogen, Helium, and Neon show behavior close to that of ideal gases. Since there are no intermolecular forces of attraction between particles of an ideal gas, it can never be liquefied. Conversely, real gases can be liquefied under certain conditions, as intermolecular forces of attraction will overcome the kinetic energy of the particles and form a liquid. Ideal Gas vs Real Gas: Similarities, Differences, and Examples Although ideal and real gases have many differences, they also have some similarities. Both are gases and are made up of particles that move randomly due to collisions with surrounding particles. This is called Brownian Motion. While ideal gases are theoretical, some real gases come close to ideal gas behavior under certain conditions. For example, Hydrogen, Oxygen, Nitrogen, Helium, and Neon show behavior that is very close to that of ideal gases at standard temperature and pressure. All gases found in the environment are real gases, even Hydrogen, Oxygen, and Nitrogen. However, they behave like real gases at low temperatures and high pressures, which is why it's possible to liquefy them. Most real gases behave like ideal gases under conditions of high temperature and low pressure. High pressure is when the particles are forced to be in close proximity, such as in CNG gas cylinders in cars or oxygen cylinders for scuba diving. The kinetic energy of gas particles is directly proportional to temperature. Higher temperature means higher kinetic energy of the gas particles, which minimizes the effect of intermolecular forces on the movement of the particles. At room temperature, gas particles have enough kinetic energy to overcome intermolecular forces and behave like ideal gases. In summary, while ideal and real gases have many differences, they also have some similarities. Understanding the ideal behavior of real gases can help us better understand how gases behave in different conditions. What is ideal and real gases? Ideal gas is a hypothetical gas which follows Ideal Gas Law at all conditions of temperature and pressure. Real gases are those which exist in the environment. They follow Ideal Gas Law only under conditions of high temperature and low pressure. What are examples of ideal and real gases? Gases like Hydrogen, Oxygen, Nitrogen, Helium Neon behave like ideal gas under conditions of Standard Temperature and Pressure (0oC, 1bar). When does a real gas behave like and ideal gases? A real gas behaves like an ideal gas under conditions of high temperature and low pressure. Why do gases exert pressure on any container they are contained in? Particles of a gas are always in random motion. They are continuously colliding with other particles and with the walls of the container. When particles collide with the container, they exert force on it. Pressure of a gas is the net force of all particles on the container walls, per unit area of the walls. Critical Phenomenon and Critical Constants Gasses can be liquefied if the temperature decreases and the pressure increases continuously, But for every s there is a characteristic temperature above which it cannot be converted to the liquid state no matter how high the pressure is. This limiting value of temperature is not the same for all gases but is different for different gases. This limiting 'value of temperature is called the critical temperature and is denoted by Tc. Hence critical temperature is defined as the temperature below which the gasses can converted into liquid on continuously increase in pressure and above which no liquefication(ie. a process of converting gas into liquid) is possible. no matter how high the pressure At the critical temperature, a certain minimum pressure has to be applied to the gas to liquefy it. This pressure is called critical pressure and is denoted by Pc may be defined as the minimum pressure which must be applied to a gas at its critical temperature to liquefy it. The volume occupied by or 2 mole of a gas at its critical temperature and critical pressure is called the critical volume and is denoted by Vc. At this stage or point, both gas and its corresponding liquid would occupy the same volume and therefore their densities are equal so, at this stage, it is not possible to distinguish between the liquid and gaseous states as the two forms are existing in equilibrium. The phenomenon of a smooth merging of a gas into its liquid state under a critical state or critical point is referred to as Critical Phenomenon' The density of the gas at the critical point is called the critical density. Tc. Pc and Vc are known as Critical Constants of the gas. Thermochemistry A branch of chemistry that describes the energy changes that occur during chemical reactions. In some situations, the energy produced by chemical reactions is actually of greater interest to chemists than the material products of the reaction. For example, the controlled combustion of organic molecules, primarily sugars and fats, within our cells provides the energy for physical activity, thought, and other complex chemical transformations that occur in our bodies. Similarly, our energy-intensive society extracts energy from the combustion of fossil fuels, such as coal, petroleum, and natural gas, to manufacture clothing and furniture, heat your home in winter and cool it in summer, and power the car or bus that gets you to class and to the movies. By the end of this chapter, you will know enough about thermochemistry to explain why ice cubes cool a glass of soda, how instant cold packs and hot packs work, and why swimming pools and waterbeds are heated. 0th Law The Zeroth Law of Thermodynamics states that if two systems are in thermodynamic equilibrium with a third system, the two original systems are in thermal equilibrium with each other. Basically, if system A is in thermal equilibrium with system C and system B is also in thermal equilibrium with system C, system A and system B are in thermal equilibrium with each other. Introduction Essentially, two systems that are in thermodynamic equilibrium will not exchange any heat. Systems in thermodynamic equilibrium will have the same temperature. In 1872 James Clerk Maxwell wrote: "If when two bodies are placed in thermal communication, one of the two bodies loses heat, and the other gains heat, that body which gives out heat is said to have a higher temperature than that which receives heat from it." And, "If when two bodies are placed in thermal communication neither of them loses or gains heat, the two bodies are said to have equal temperature or the same temperature. The two bodies are then said to be in thermal equilibrium." Maxwell also stated, "Bodies whose temperatures are equal to that of the same body have themselves equal temperatures." In 1897 Max Planck said, "If a body, A, be in thermal equilibrium with two other bodies, B and C, then B and C are in thermal equilibrium with one another." Exercise 1 kg of water at 10º C is added to 10 kg of water at 50º C. What is the temperature of the water when it reaches thermal equilibrium? 1st law To understand and perform any sort of thermodynamic calculation, we must first understand the fundamental laws and concepts of thermodynamics. For example, work and heat are interrelated concepts. Heat is the transfer of thermal energy between two bodies that are at different temperatures and is not equal to thermal energy. Work is the force used to transfer energy between a system and its surroundings and is needed to create heat and the transfer of thermal energy. Both work and heat together allow systems to exchange energy. The relationship between the two concepts can be analyzed through the topic of Thermodynamics, which is the scientific study of the interaction of heat and other types of energy. Introduction To understand the relationship between work and heat, we need to understand a third, linking factor: the change in internal energy. Energy cannot be created nor destroyed, but it can be converted or transferred. Internal energy refers to all the energy within a given system, including the kinetic energy of molecules and the energy stored in all of the chemical bonds between molecules. With the interactions of heat, work and internal energy, there are energy transfers and conversions every time a change is made upon a system. However, no net energy is created or lost during these transfers. The First Law of Thermodynamics states that energy can be converted from one form to another with the interaction of heat, work and internal energy, but it cannot be created nor destroyed, under any circumstances. Mathematically, this is represented as ΔU=q+w  ΔU is the total change in internal energy of a system,  q is the heat exchanged between a system and its surroundings, and  w is the work done by or on the system. The internal energy of a system would decrease if the system gives off heat or does work. Therefore, internal energy of a system increases when the heat increases (this would be done by adding heat into a system). The internal energy would also increase if work were done onto a system. Any work or heat that goes into or out of a system changes the internal energy. However, since energy is never created nor destroyed (thus, the first law of thermodynamics), the change in internal energy always equals zero. If energy is lost by the system, then it is absorbed by the surroundings. If energy is absorbed into a system, then that energy was released by the surroundings: Work is also equal to the negative external pressure on the system multiplied by the change in volume: w=−pΔV where P is the external pressure on the system, and ΔV is the change in volume. This is specifically called "pressure-volume" work. The internal energy of a system would decrease if the system gives off heat or does work. Therefore, internal energy of a system increases when the heat increases (this would be done by adding heat into a system). The internal energy would also increase if work were done onto a system. Any work or heat that goes into or out of a system changes the internal energy. However, since energy is never created nor destroyed (thus, the first law of thermodynamics), the change in internal energy always equals zero. If energy is lost by the system, then it is absorbed by the surroundings. If energy is absorbed into a system, then that energy was released by the surroundings: ΔUsystem=−ΔUsurroundings where ΔUsystem is the total internal energy in a system, and ΔUsurroundings is the total energy of the surroundings. Example A gas in a system has constant pressure. The surroundings around the system lose 62 J of heat and does 474 J of work onto the system. What is the internal energy of the system? The Second Law of Thermodynamics states that the state of entropy of the entire universe, as an isolated system, will always increase over time. The second law also states that the changes in the entropy in the universe can never be negative. Introduction Why is it that when you leave an ice cube at room temperature, it begins to melt? Why do we get older and never younger? And, why is it whenever rooms are cleaned, they become messy again in the future? Certain things happen in one direction and not the other, this is called the "arrow of time" and it encompasses every area of science. The thermodynamic arrow of time (entropy) is the measurement of disorder within a system. Denoted as ΔSΔ , the change of entropy suggests that time itself is asymmetric with respect to order of an isolated system, meaning: a system will become more disordered, as time increases. The 3rd law of thermodynamics will essentially allow us to quantify the absolute amplitude of entropies. It says that when we are considering a totally perfect (100% pure) crystalline structure, at absolute zero (0 Kelvin), it will have no entropy (S). Note that if the structure in question were not totally crystalline, then although it would only have an extremely small disorder (entropy) in space, we could not precisely say it had no entropy. One more thing, we all know that at zero Kelvin, there will still be some atomic motion present, but to continue making sense of this world, we have to assume that at absolute Kelvin there is no entropy whatsoever. Calorimetry Thermal energy itself cannot be measured easily, but the temperature change caused by the flow of thermal energy between objects or substances can be measured. Calorimetry describes a set of techniques employed to measure enthalpy changes in chemical processes using devices called calorimeters. To have any meaning, the quantity that is actually measured in a calorimetric experiment, the change in the temperature of the device, must be related to the heat evolved or consumed in a chemical reaction. We begin this section by explaining how the flow of thermal energy affects the temperature of an object. Heat Capacity We have seen that the temperature of an object changes when it absorbs or loses thermal energy. The magnitude of the temperature change depends on both the amount of thermal energy transferred (q) and the heat capacity of the object. Its heat capacity (C) is the amount of energy needed to raise the temperature of the object exactly 1°C; the units of C are joules per degree Celsius (J/°C). Note that a degree Celsius is exactly the same as a Kelvin, so the heat capacities can be expresses equally well, and perhaps a bit more correctly in SI, as joules per Kelvin, J/K The change in temperature (ΔT) is ΔT=qC Where q is the amount of heat (in joules), C is the heat capacity (in joules per degree Celsius), and ΔT is Tfinal−Tinitialin degrees Celsius). The value of C is intrinsically a positive number, but ΔT and q can be either positive or negative, and they both must have the same sign. If ΔT and q are positive, then heat flows from The surroundings into an object. If ΔT and q are negative, then heat flows from an object into its surroundings. Heat Capacity The heat capacity of a substance can be defined as the amount of heat required to change its temperature by one degree.  Heat energy is the measure of the total internal energy of a system. This includes the total kinetic energy of the system and the potential energy of the molecules.  It has been seen that the internal energy of a system can be changed by either supplying heat energy to it, or doing work on it.  The internal energy of a system is found to increase with the increase in temperature. This increase in internal energy depends on the temperature difference, the amount of matter, etc.  Heat capacity is defined as the amount of heat energy required to raise the temperature of a given quantity of matter by one degree Celsius.  Heat capacity for a given matter depends on its size or quantity and hence it is an extensive property. The unit of heat capacity is joule per Kelvin or joule per degree Celsius. Mathematically, Q=CΔT Where Q is the heat energy required to bring about a temperature change of ΔT and C is the heat capacity of the system under study. Specific Heat Capacity Scientists needed a quantity that has no dependence on the quantity or size of matter under consideration for thermodynamic studies this made them define specific heat capacity. It is an intensive property as it is independent of the quantity or size of the matter. Specific heat capacity for any substance or matter can be defined as the amount of heat energy required to raise the temperature of a unit mass of that substance by one degree Celsius. Mathematically it is given as: Q= m c ΔT Here Q is the amount of heat energy required to change the temperature of m (kg) of a substance by ΔT, s is the specific heat capacity of the system. Thermodynamics continues to play a vital role in our lives directly or indirectly. Scientists and engineers use the laws of thermodynamics to design new processes for reactions that would have high efficiency and product yield. Chemical and mechanical engineers apply the concepts of thermodynamics for designing heat engines with high efficiency and better outputs. What are Heat Capacity C, Cp, and Cv? Definition of molar Heat Capacity (C) The total amount of energy in the form of heat needed to increase the temperature of 1 mole of any substance by 1 unit is called the molar heat capacity (C) of that substance. It also significantly depends on the nature, size and composition of a substance in a system. q = n C ∆T Where,  q is the heat supplied or needed to bring about a change in temperature (∆T) in 1 mole of any given substance,  n is the amount in moles,  The constant C is known as the molar heat capacity of the body of the given substance. Cp In a system, Cp is the amount of heat energy released or absorbed by a unit mass of the substance with the change in temperature at a constant pressure. In other words, under constant pressure, it is the heat energy transfer between a system and its surroundings. So, Cp represents the molar heat capacity, C when pressure is constant. The change in temperature will always cause a change in the enthalpy of the system. Enthalpy (∆H) is the heat energy absorbed or released by the system. Furthermore, enthalpy change occurs during the change of phase or state of a substance. For example, when a solid changes to its liquid form (i.e., the change from ice to water), the enthalpy change is called the heat of fusion. When a liquid changes to its gaseous form (i.e., the change from water to water vapour), the enthalpy change is called heat vaporisation. The system absorbs or releases heat without the change in pressure in that substance, then its specific heat at constant pressure, Cp can be written as: Cp=[dH/dT]p where Cp represents the specific heat at constant pressure; dH is the change in enthalpy; dT is the change in temperature. Cv During a small change in the temperature of a substance, Cv is the amount of heat energy absorbed/released per unit mass of a substance where volume does not change. In other words, Cv is the heat energy transfer between a system and its surroundings without any change in the volume of that system. Cv represents the molar heat capacity C when the volume is constant. Under a constant volume, the volume of a substance does not change, so the change in volume is zero. As the term is related to the internal energy of a system, which is the total of both potential energy and kinetic energy of that system. The system absorbs or releases heat without change in volume of that substance, then its specific heat at constant volume, Cv can be: Cv=[dU/dT]v Where,  Cv represents the specific heat at constant volume;  dU is the small change in the internal energy of the system;  dT is the change in temperature of the system. Relationship Between Cp and Cv The following relationship can be given considering the ideal gas behaviour of a gas. Cp−Cv=R Where, R is called the universal gas constant. Heat Capacity Ratio In thermodynamics, the heat capacity ratio or ratio of specific heat capacities (Cp:Cv) is also known as the adiabatic index. It is the ratio of two specific heat capacities, Cp and Cv is given by: The Heat Capacity at Constant Pressure (Cp)/ Heat capacity at Constant Volume(Cv) The isentropic expansion factor is another name for heat capacity ratio that is also denoted for an ideal gas by γ (gamma). Therefore, the ratio between Cp and Cv is the specific heat ratio, γ. So, γ=Cp/Cv REVERSIBLE PROCESS  A reversible process is a process in which the system and environment can be restored to exactly the same initial states that they were in before the process occurred, if we go backward along the path of the process. The necessary condition for a reversible process is therefore the quasi-static requirement. Note that it is quite easy to restore a system to its original state; the hard part is to have its environment restored to its original state at the same time. For example, in the example of an ideal gas expanding into vacuum to twice its original volume, we can easily push it back with a piston and restore its temperature and pressure by removing some heat from the gas. The problem is that we cannot do it without changing something in its surroundings, such as dumping some heat there. A reversible process is truly an ideal process that rarely happens. We can make certain processes close to reversible and therefore use the consequences of the corresponding reversible processes as a starting point or reference. In reality, almost all processes are irreversible, and some properties of the environment are altered when the properties of the system are restored. The expansion of an ideal gas, as we have just outlined, is irreversible because the process is not even quasi-static, that is, not in an equilibrium state at any moment of the expansion. From the microscopic point of view, a particle described by Newton’s second law can go backward if we flip the direction of time. But this is not the case, in practical terms, in a macroscopic system with more than 1023 particles or molecules, where numerous collisions between these molecules tend to erase any trace of memory of the initial trajectory of each of the particles. For example, we can actually estimate the chance for all the particles in the expanded gas to go back to the original half of the container, but the current age of the universe is still not long enough for it to happen even once. IRREVERSIBLE PROCESS An irreversible process is what we encounter in reality almost all the time. The system and its environment cannot be restored to their original states at the same time. Because this is what happens in nature, it is also called a natural process. The sign of an irreversible process comes from the finite gradient between the states occurring in the actual process. For example, when heat flows from one object to another, there is a finite temperature difference (gradient) between the two objects. More importantly, at any given moment of the process, the system most likely is not at equilibrium or in a well-defined state. This phenomenon is called irreversibility. Let us see another example of irreversibility in thermal processes. Consider two objects in thermal contact: one at temperature T1 and the other at temperature T2>T1, as shown in figure Spontaneous heat flow from an object at higher temperature T2 to another at lower temperature T1. We know from common personal experience that heat flows from a hotter object to a colder one. For example, when we hold a few pieces of ice in our hands, we feel cold because heat has left our hands into the ice. The opposite is true when we hold one end of a metal rod while keeping the other end over a fire. Based on all of the experiments that have been done on spontaneous heat transfer, the following statement summarizes the governing principle: Heat never flows spontaneously from a colder object to a hotter object. This statement turns out to be one of several different ways of stating the second law of thermodynamics. The form of this statement is credited to German physicist Rudolf Clausius (1822−1888) and is referred to as the Clausius statement of the second law of thermodynamics. The word “spontaneously” here means no other effort has been made by a third party, or one that is neither the hotter nor colder object. We will introduce some other major statements of the second law and show that they imply each other. In fact, all the different statements of the second law of thermodynamics can be shown to be equivalent, and all lead to the irreversibility of spontaneous heat flow between macroscopic objects of a very large number of molecules or particles. Both isothermal and adiabatic processes sketched on a pV graph are reversible in principle because the system is always at an equilibrium state at any point of the processes and can go forward or backward along the given curves. Other idealized processes can be represented by pV curves; summarizes the most common reversible processes.  Process Constant Quantity and Resulting Fact Constant pressure W=pΔV Isobaric Isochoric Constant volume W=0 Isothermal Constant temperature ΔT=0 Adiabatic No heat transfer Q=0 Clausius statement of the second law of thermodynamics “heat never flows spontaneously from a colder object to a hotter object”  A mole of an ideal gas at pressure 4.00 atm and temperature 298 K expands isothermally to double its volume. What is the work done by the gas? Solution: Work done is W= -nRTln(Vf/Vi) PV=nRT n=PV/RT The work done by the gas is approximately -2.7724 L atm  A mole of ideal monatomic gas at 0 °C and 1.00 atm is warmed to expand isobarically to triple its volume. How much heat is transferred during the process? Solution: As we know that heat transfer during process is ΔQ = ΔU + ΔW Isobaric, so ΔW = PΔV The internal energy of an ideal monatomic gas is given by: U = (3/2)nRT1 (V2 / V1) = (T2 / T1) In this case, V2 = 3 * V1 (tripling the volume) Now that we have T2, we can find the final internal energy (U2): U2 = (3/2)nRT2, Now, calculate ΔU, ΔU = U2 - U1 ΔW = PΔV P remains constant at 1.00 atm, which is equivalent to 101.325 kPa or 101325 Pa ΔQ = ΔU + ΔW Gibbs Free Energy  Gibbs free energy is the maximum work done by the system at constant temperature and pressure Gibbs free energy is associated with internal energy, entropy and PV Change in Gibbs free energy ∆𝐺 = ∆𝐻 − 𝑇∆𝑆 Free energy, G, denotes the self intrinsic electrostatic potential energy of a system. This means that in any molecule if we calculate the total electrostatic potential energy of all the charges due to all the other charges, we get what is called the free energy of the molecule. It tells about the stability of a molecule with respect to another molecule. Lesser the free energy of a molecule more stable it is. Every reaction proceeds with a decrease in free energy. The free energy change in a process is expressed by ΔG If it is negative, it means that products have lesser G than reactants, so the reaction goes forward. If it is positive the reaction goes reverse and if it is zero the reaction is at equilibrium. ΔG is the free energy change at any given concentration of reactants and products. If all the reactants and products are taken at a concentration of 1 mole per liter, the free energy change of the reaction is called ΔG° (standard free energy change). One must understand that ΔG° is not the free energy change at equilibrium. It is the free energy change when all the reactants and products are at a concentration of 1 mole/L. Equilibrium Constant Equilibrium constant of concentration is a ratio of concentration of products over reactant of a reaction which is at equilibrium. [𝑃 ]𝑝 𝐾= [𝑅 ]𝑟 Both Gibbs free energy and equilibrium constant can be used to determine the spontaneity of reaction  ∆𝐺 = ∆𝐺 𝑜 + 𝑅𝑇𝑙𝑛𝑄 ∆𝐺 (when equilibrium has not been attained) is related to the standard Gibbs free energy of the reaction ∆𝐺 𝑜 and reaction quotient Q. When equilibrium is attained, there is no further free energy change, i.e. ∆𝐺 = 0 and Q becomes equal to equilibrium constant. Hence the above equation becomes ∆𝐺 𝑜 = −𝑅𝑇𝑙𝑛𝐾 The units of ΔG° depends only on RT. T is always in Kelvin , and if R is in Joules, ΔG° will be in joules , and if R is calories then ΔG° will be in calories. If ∆𝐺 𝑜 is negative and value of K is high reaction is spontaneous and if ∆𝐺 𝑜 is positive and K is low reaction is spontaneous is backward direction. If ∆𝐺 𝑜 is zero and value of K is near to zero reaction is at equilibrium. Gibbs–Helmholtz equation The Gibbs–Helmholtz equation is a thermodynamic equation used for calculating changes in the Gibbs energy of a system as a function of temperature. It is named after Josiah Willard Gibbs and Hermann von Helmholtz. Equation where H is the enthalpy, T the absolute temperature and G the Gibbs free energy of the system, all at constant pressure p. The equation states that the change in the G/T ratio at constant pressure as a result of an infinitesimally small change in temperature is a factor H/T2. The typical applications are to chemical reactions. The equation reads: with ΔG as the change in Gibbs energy and ΔH as the enthalpy change (considered independent of temperature). The o denotes standard pressure (1 bar) with ΔG as the change in Gibbs energy and ΔH as the enthalpy change (considered independent of temperature). The o denotes standard pressure (1 bar). Integrating with respect to T (again p is constant) it becomes: This equation quickly enables the calculation of the Gibbs free energy change for a chemical reaction at any temperature T2 with knowledge of just the Standard Gibbs free energy change of formation and the Standard enthalpy change of formation for the individual components. Also, using the reaction isotherm equation, that is which relates the Gibbs energy to a chemical equilibrium constant, the van 't Hoff equation can be derived. Equilibrium Constant Expressions Reactions don't stop when they come to equilibrium. But the forward and reverse reactions are in balance at equilibrium, so there is no net change in the concentrations of the reactants or products, and the reaction appears to stop on the macroscopic scale. Chemical equilibrium is an example of a dynamic balance between opposing forces the forward and reverse reactions not a static balance. Let's look at the logical consequences of the assumption that the reaction between ClNO2 and NO eventually reaches equilibrium. The rates of the forward and reverse reactions are the same when this system is at equilibrium. At equilibrium: rateforward = ratereverse Substituting the rate laws for the forward and reverse reactions into this equality gives the following result. At equilibrium: kf(ClNO2)(NO) = kr(NO2)(ClNO) But this equation is only valid when the system is at equilibrium, so we should replace the (ClNO2), (NO), (NO2), and (ClNO) terms with symbols that indicate that the reaction is at equilibrium. By convention, we use square brackets for this purpose. The equation describing the balance between the forward and reverse reactions when the system is at equilibrium should therefore be written as follows. At equilibrium: kf[ClNO2][NO] = kr[NO2][ClNO] Rearranging this equation gives the following result. Since kf and kr are constants, the ratio of kf divided by kr must also be a constant. This ratio is the equilibrium constant for the reaction, Kc. The ratio of the concentrations of the reactants and products is known as the equilibrium constant expression. No matter what combination of concentrations of reactants and products we start with, the reaction will reach equilibrium when the ratio of the concentrations defined by the equilibrium constant expression is equal to the equilibrium constant for the reaction. We can start with a lot of ClNO2 and very little NO, or a lot of NO and very little ClNO2. It doesn't matter. When the reaction reaches equilibrium, the relationship between the concentrations of the reactants and products described by the equilibrium constant expression will always be the same. At 25oC, this reaction always reaches equilibrium when the ratio of these concentrations is 1.3 x 104. The procedure used in this section to derive the equilibrium constant expression only works with reactions that occur in a single step, such as the transfer of a chlorine atom from ClNO2 to NO. Many reactions take a number of steps to convert reactants into products. But any reaction that reaches equilibrium, no matter how simple or complex, has an equilibrium constant expression that satisfies the rules in the following section. Rules for Writing Equilibrium Constant Expressions  Even though chemical reactions that reach equilibrium occur in both directions, the reagents on the right side of the equation are assumed to be the "products" of the reaction and the reagents on the left side of the equation are assumed to be the "reactants."  The products of the reaction are always written above the line in the numerator.  The reactants are always written below the line in the denominator.  For homogeneous systems, the equilibrium constant expression contains a term for every reactant and every product of the reaction.  The numerator of the equilibrium constant expression is the product of the concentrations of the "products" of the reaction raised to a power equal to the coefficient for this component in the balanced equation for the reaction.   The denominator of the equilibrium constant expression is the product of the concentrations of the "reactants" raised to a power equal to the coefficient for this component in the balanced equation for the reaction. Altering or Combining Equilibrium Reactions What happens to the magnitude of the equilibrium constant for a reaction when we turn the equation around? Consider the following reaction, for example. ClNO2(g) + NO(g) NO2(g) + ClNO(g) The equilibrium constant expression for this equation is written as follows. Because this is a reversible reaction, it can also be represented by an equation written in the opposite direction. NO2(g) + ClNO(g) ClNO2(g) + NO(g) The equilibrium constant expression is now written as follows. Each of these equilibrium constant expressions is the inverse of the other. We can therefore calculate Kc´ by dividing Kc into 1. We can also calculate equilibrium constants by combining two or more reactions for which the value of Kc is known. Assume, for example, that we know the equilibrium constants for the following gas-phase reactions at 200oC. N2(g) + O2(g) 2 NO(g) Kc1 = 2.3 x 10-19 2 NO(g) + O2(g) 2 NO2(g) Kc2 = 3 x 106 We can combine these reactions to obtain an overall equation for the reaction between N2 and O2 to form NO2. N2(g) + O2(g) 2 NO(g)  + 2 NO(g) + O2(g) 2 NO2(g) ______________________________________________________________ N2(g) + 2 O2(g) 2 NO2(g) It is easy to show that the equilibrium constant expression for the overall reaction is equal to the product of the equilibrium constant expressions for the two steps in this reaction. The equilibrium constant for the overall reaction is therefore equal to the product of the equilibrium constants for the individual steps. Kc = Kc1 x Kc2 = (2.3 x 10-19)(3 x 106) = 7 x 10-13 Reaction Quotients: A Way to Decide Whether a Reaction is at Equilibrium We have a model that describes what happens when a reaction reaches equilibrium: At the molecular level, the rate of the forward reaction is equal to the rate of the reverse reaction. Since the reaction proceeds in both directions at the same rate, there is no apparent change in the concentrations of the reactants or the products on the macroscopic scale the level of objects visible to the naked eye. This model can also be used to predict the direction in which a reaction has to shift to reach equilibrium. If the concentrations of the reactants are too large for the reaction to be at equilibrium, the rate of the forward reaction will be faster than the reverse reaction, and some of the reactants will be converted into products until equilibrium is achieved. Conversely, if the concentrations of the reactants are too small, the rate of the reverse reaction will exceed that of the forward reaction, and the reaction will convert some of the excess products back into reactants until the system reaches equilibrium. We can determine the direction in which a reaction has to shift to reach equilibrium by calculating the reaction quotient (Qc) for the reaction. The reaction quotient is defined as the product of the concentrations of the products of the reaction divided by the product of the concentration of the reactants at any moment in time. To illustrate how the reaction quotient is used, let's consider the following gas-phase reaction. H2(g) + I2(g) 2 HI(g) The equilibrium constant expression for this reaction is written as follows. By analogy, we can write the expression for the reaction quotient as follows. Qc can take on any value between zero and infinity. If the system contains a great deal of HI and very little H2 and I2, the reaction quotient is very large. If the system contains relatively little HI and a great deal of H2 and I2, the reaction quotient is very small. At any moment in time, there are three possibilities. 1. Qc is smaller than Kc. The system contains too much reactant and not enough product to be at equilibrium. The value of Qc must increase in order for the reaction to reach equilibrium. Thus, the reaction has to convert some of the reactants into products to come to equilibrium. 2. Qc is equal to Kc. If this is true, then the reaction is at equilibrium. 3. Qc is larger than Kc. The system contains too much product and not enough reactant to be at equilibrium. The value of Qc must become smaller before the reaction can come to equilibrium. Thus, the reaction must convert some of the products into reactants to reach equilibrium. Practice Problem Assume that the concentrations of H2, I2, and HI can be measured for the following reaction at any moment in time. H2(g) + I2(g) 2 HI(g) Kc = 60 For each of the following sets of concentrations, determine whether the reaction is at equilibrium. If it isn't, decide in which direction it must go to reach equilibrium. (a) (H2) = (I2) = (HI) = 0.010 M (b) (HI) = 0.30 M; (H2) = 0.01 M; (I2) = 0.15 M (c) (H2) = (HI) = 0.10 M; (I2) = 0.0010 M  Changes in Concentration that Occur as a Reaction Comes to Equilibrium The relative size of Qc and Kc for a reaction tells us whether the reaction is at equilibrium at any moment in time. If it isn't, the relative size of Qc and Kc tell us the direction in which the reaction must shift to reach equilibrium. Equilibrium Constant for Predicting the Extent of Reaction The ratio of the concentration of products and reactants at equilibrium. This article highlights the equilibrium constant for predicting the extent of reaction. Laws of chemical equilibrium and constant can be expressed in mathematical expressions giving a brief about the reaction in equilibrium. It can be expressed as the value of the reaction quotient, which cannot be changed further by any reaction. A general reaction represents: A+B =C+D In which equilibrium is maintained between the reactants ( A & B ) and products ( C & D ), respectively. The chemical equilibrium constant K represents the relationship between the active reactants and the products. This article explains the equilibrium constant for predicting the extent of reaction. Law of mass action According to the equilibrium constant for predicting the extent of reaction, the law of mass action states the following: At equilibrium, the rate of the two opposing reactions becomes equal i.e. Rate of forwarding reaction = Rate of backward reaction. K = k1 (forward) / k2 (backward) At a particular temperature, K1 & K2 are constants. Therefore, the ratio K1 / K2 will be a constant. This is represented as K and is called the equilibrium constant. Thus, K = K1 / K2 K1 / K2 = (C) (D) / (A) (B) The magnitude of the equilibrium constant K helps predict the extent to which a reaction proceeds. Temperature is directly proportional to the rate of reaction between the reactants and the products formed. An increase in temperature proportionally increases the rate of reaction. A+B =C+D K = k1 (forward) / k2 (backward) In the above reactions, where k1 and k2 are rates of constants for the forward and backward reactions, respectively, K is the equilibrium constant. Here, (A) (B) (C) & (D) represent the active masses of concentration of A, B, C & D, respectively, at equilibrium.  Equilibrium Constant For Predicting The Extent Of Reaction When we deal with reversible reactions, it is important to figure out the reaction direction at any given point. We can predict the extent of the reaction by finding the reaction quotient and equilibrium constant. A high KC value indicates that the reaction has reached equilibrium with a high product yield, whereas a low KC value indicates that the reaction has reached equilibrium with a low product yield. If KC > 103, the reaction is nearly complete. If KC 1, then equilibrium favours products. If K < 1, then equilibrium favours the reactants. The equilibrium constant cannot be zero because it implies zero at being in equilibrium. Conclusion The reaction rate depends on the magnitude, velocity, physical nature and temperature of the reactants placed. The magnitude of the equilibrium constant K indicates the rate of reaction to which the reaction is proceeding. An increase in K indicates an increase in products’ equilibrium concentration. Reaction extent is the quantity that informs us how much the reaction has extended. The constant K measures the reactants infused to react and form the products. This article highlights the equilibrium constant for predicting the extent of reaction and the equilibrium constant for predicting the extent of reaction importance. Gibbs energies of formation and calculations of equilibrium constants We have identified three criteria for whether a given reaction will occur spontaneously (that is, proceed in the forward direction, as written, to reach equilibrium): ΔS univ > 0, ΔGsys < 0, and the relative magnitude of the reaction quotient Q versus the equilibrium constant K. Recall that if K > Q, then the reaction proceeds spontaneously to the right as written, resulting in the net conversion of reactants to products. Conversely, if K < Q, then the reaction proceeds spontaneously to the left as written, resulting in the net conversion of products to reactants. If K = Q, then the system is at equilibrium, and no net reaction occurs. Table 11 summarizes these criteria and their relative values for spontaneous, nonspontaneous, and equilibrium processes. Criteria for the Spontaneity of a Process as Written Because all three criteria are assessing the same thing—the spontaneity of the process—it would be most surprising indeed if they were not related. In this section, we explore the relationship between the free energy change of reaction (ΔG) and the instantaneous reaction quotient (Qc). To do so, we will first reveal the relationship between the standard free energy change of a reaction (ΔG°) and the equilibrium constant (Kc). Free Energy and the Equilibrium Constant Because ΔH° and ΔS° determine the magnitude of ΔG° and because K is a measure of the ratio of the concentrations of products to the concentrations of reactants, we should be able to express K in terms of ΔG° and vice versa. Combining terms gives the following relationship between ΔG and the reaction quotient Qc: ΔG=ΔG∘+RTlnQ=ΔG∘+RTlnQ where ΔG° indicates that all reactants and products are in their standard states. For a system at equilibrium (Kc=Qc,), and ΔG = 0 for a system at equilibrium. Therefore, we can describe the relationship between ΔG° and K as follows: 0=ΔG°+RTlnKc ΔG°=−RTlnKc If you combine equations, you get the equation ΔG=RTlnQcKc If the products and reactants are in their standard states and ΔG° < 0, then K > 1, and products are favored over reactants at equilibrium. Conversely, if ΔG° > 0, then K < 1, and reactants are favored over products at equilibrium. If ΔG° = 0, then K=1, and neither reactants nor products are favored at equilibrium. ΔG° is −32.7 kJ/mol of N2 for the reaction at 100oC N2(g)+3H2(g)⇌2NH3(g) Calculate ΔG for the same reaction under the following nonstandard conditions:  [N2][N2] = 2.00 M,  [H2][H2] = 7.00 M,  [NH3][NH3] = 0.021 M,  and T = 100°C. In which direction must the reaction proceed to reach equilibrium? Solution: A Using the equilibrium constant expression for the given reaction, we can calculate Q: Qc=[NH3]2[N2][H2]3=(0.021)2(2.00)(7.00)3=6.4×10−7 B Using the value of ΔG°, calculate the value of K ΔGo=−32,700J=−(8.314Jg⋅K)(373K)lnKc −32,700J−8.314Jg⋅K⋅373K=lnKc e10.54=38,000J=Kc C Substituting the values of K and Q into Equation 11, ΔG=RTlnQK=(8.314J/K)(373K)(1kJ1000J)ln6.4×10−73.8×104 =−77 kJ2=−77 kJ2 Because ΔG < 0 and K > Q, the reaction is spontaneous in the forward direction, as written. In other words, the reaction must proceed to the right to reach equilibrium. Temperature Dependence of the Equilibrium Constant The fact that ΔG° and K are related provides us with another explanation of why equilibrium constants are temperature dependent. This relationship is shown explicitly in Equation 33, which can be rearranged as follows: lnKc=−ΔH∘RT+ΔS∘R Assuming ΔH° and ΔS° are temperature independent, for an exothermic reaction (ΔH° < 0), the magnitude of K decreases with increasing temperature, whereas for an endothermic reaction (ΔH° > 0), the magnitude of K increases with increasing temperature. The quantitative relationship expressed in Equation agrees with the qualitative predictions made by applying Le Chatelier’s principle. Because heat is produced in an exothermic reaction, adding heat (by increasing the temperature) will shift the equilibrium to the left, favoring the reactants and decreasing the magnitude of K. Conversely, because heat is consumed in an endothermic reaction, adding heat will shift the equilibrium to the right, favoring the products and increasing the magnitude of K. Equation also shows that the magnitude of ΔH° dictates how rapidly K changes as a function of temperature. In contrast, the magnitude and sign of ΔS° affect the magnitude of K but not its temperature dependence. If we know the value of Kc at a given temperature and the value of ΔH° for a reaction, we can estimate the value of Kc at any other temperature, even in the absence of information on ΔS°. Suppose, for example, that K1 and K2 are the equilibrium constants for a reaction at temperatures T1 and T2, respectively. Applying Equation gives the following relationship at each temperature: Thus calculating ΔH° from tabulated enthalpies of formation and measuring the equilibrium constant at one temperature (K1) allow us to calculate the value of the equilibrium constant at any other temperature (K2), assuming that ΔH° and ΔS° are independent of temperature. Both K and ΔG° can be used to predict the ratio of products to reactants at equilibrium for a given reaction. ΔG° is related to K by the equation ΔG°=−RTlnKc.  If ΔG° < 0, then K > 1, and products are favored over reactants at equilibrium.  If ΔG° > 0, then K < 1, and reactants are favored over products at equilibrium.  If ΔG° = 0, then K = 1, and the amount of products will be roughly equal to the amount of reactants at equilibrium. This is a rare occurrence for chemical reactions. If a system is not at equilibrium, ΔG and Q can be used to tell us in which direction the reaction must proceed to reach equilibrium. ΔG is related to Q by the equation ΔG=RTlnQcKc  If ΔG < 0, then K > Q, and the reaction must proceed to the right to reach equilibrium.  If ΔG > 0, then K < Q, and the reaction must proceed to the left to reach equilibrium.  If ΔG = 0, then K = Q, and the reaction is at equilibrium. We can use the measured equilibrium constant Kc at one temperature, along with ΔH° to estimate the equilibrium constant for a reaction at any other temperature. Van 't Hoff equation The Van 't Hoff equation relates the change in the equilibrium constant, Kc, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, ΔH⊖, for the process. It was proposed by Dutch chemist Jacabus Henricus Van’t Hoff in 1884. The Van 't Hoff equation has been widely utilized to explore the changes in state function in a thermodynamic system. The Van 't Hoff plot, which is derived from this equation, is especially effective in estimating the change in enthalpy and entropy of a chemical reaction. We can use Gibbs-Helmholtz to get the temperature dependence of Kc At equilibrium, we can equate ΔGo to −RTlnKc so we get: We see that whether Kc increases or decreases with temperature is linked to whether the reaction enthalpy is positive or negative. If temperature is changed little enough that ΔHo can be considered constant, we can translate a Kc value at one temperature into another by integrating the above expression, we get a similar derivation as with melting point depression: If more precision is required we could correct for the temperature changes of ΔHo by using heat capacity data. How Kc increases or decreases with temperature is linked to whether the reaction enthalpy is positive or negative. The expression for Kc is a rather sensitive function of temperature given its exponential dependence on the difference of stoichiometric coefficients One way to see the sensitive temperature dependence of equilibrium constants is to recall that However, since under constant pressure and temperature Equation becomes Taking the natural log of both sides, we obtain a linear relation which is known as the van ’t Hoff equation. It shows that a plot f lnK vs. 1/T should be a line with slope −ΔHo/R and intercept ΔSo/R Hence, these quantities can be determined from the lnK vs. 1/T data without doing calorimetry. Of course, the main assumption here is that ΔHo and ΔSo are only very weakly dependent on T, which is usually valid. Le Chatelier's principle An action that changes the temperature, pressure, or concentrations of reactants in a system at equilibrium stimulates a response that partially offsets the change while a new equilibrium condition is established. Hence, Le Châtelier's principle states that any change to a system at equilibrium will adjust to compensate for that change. In 1884 the French chemist and engineer Henry-Louis Le Châtelier proposed one of the central concepts of chemical equilibria, which describes what happens to a system when something briefly removes it from a state of equilibrium. It is important to understand that Le Châtelier's principle is only a useful guide to identify what happens when the conditions are changed in a reaction in dynamic equilibrium; it does not give reasons for the changes at the molecular level (e.g., timescale of change and underlying reaction mechanism). Concentration Changes Le Châtelier's principle states that if the system is changed in a way that increases the concentration of one of the reacting species, it must favor the reaction in which that species is consumed. In other words, if there is an increase in products, the reaction quotient, Qc, is increased, making it greater than the equilibrium constant, Kc. Consider an equilibrium established between four substances, A, B, C, and D: A+2B⇌C+D Increasing a concentration What happens if conditions are altered by increasing the concentration of A? According to Le Châtelier, the position of equilibrium will move in such a way as to counteract the change. In this case, the equilibrium position will move so that the concentration of A decreases again by reacting it with B to form more C and D. The equilibrium moves to the right (indicated by the green arrow below). In a practical sense, this is a useful way of converting the maximum possible amount of B into C and D; this is advantageous if, for example, B is a relatively expensive material whereas A is cheap and plentiful. Decreasing a concentration In the opposite case in which the concentration of A is decreased, according to Le Châtelier, the position of equilibrium will move so that the concentration of A increases again. More C and D will react to replace the A that has been removed. The position of equilibrium moves to the left. This is essentially what happens if one of the products is removed as soon as it is formed. If, for example, C is removed in this way, the position of equilibrium would move to the right to replace it. If it is continually removed, the equilibrium position shifts further and further to the right, effectively creating a one-way, irreversible reaction. Pressure Changes This only applies to reactions involving gases, although not necessarily all species in the reaction need to be in the gas phase. A general homogeneous gaseous reaction is given below: A(g)+2B(g)⇌C(g)+D(g) Increasing the pressure According to Le Châtelier, if the pressure is increased, the position of equilibrium will move so that the pressure is reduced again. Pressure is caused by gas molecules hitting the sides of their container. The more molecules in the container, the higher the pressure will be. The system can reduce the pressure by reacting in such a way as to produce fewer molecules. In this case, there are three moles on the left-hand side of the equation, but only two on the right. By forming more C and D, the system causes the pressure to reduce. Increasing the pressure on a gas reaction shifts the position of equilibrium towards the side with fewer moles of gas molecules. Haber Process N2+3H2⇌2NH3 If this mixture is transferred from a 1.5 L flask to a 5 L flask, in which direction does a net change occur to return to equilibrium? Solution Because the volume is increased (and therefore the pressure reduced), the shift occurs in the direction that produces more moles of gas. To restore equilibrium the shift needs to occur to the left, in the direction of the reverse reaction. Decreasing the pressure The equilibrium will move in such a way that the pressure increases again. It can do that by producing more gaseous molecules. In this case, the position of equilibrium will move towards the left-hand side of the reaction. What happens if there are the same number of molecules on both sides of the equilibrium reaction? In this case, increasing the pressure has no effect on the position of the equilibrium. Because there are equal numbers of molecules on both sides, the equilibrium cannot move in any way that will reduce the pressure again. Again, this is not a rigorous explanation of why the position of equilibrium moves in the ways described. A mathematical treatment of the explanation can be found on this page. Summary of Pressure Effects Three ways to change the pressure of an equilibrium mixture are: 1. Add or remove a gaseous reactant or product, 2. Add an inert gas to the constant-volume reaction mixture, or 3. Change the volume of the system. 1. Adding products makes Qc greater than Kc. This creates a net change in the reverse direction, toward reactants. The opposite occurs when adding more reactants. 2. Adding an inert gas into a gas-phase equilibrium at constant volume does not result in a shift. This is because the addition of a non-reactive gas does not change the partial pressures of the other gases in the container. While the total pressure of the system increases, the total pressure does not have any effect on the equilibrium constant. 3. When the volume of a mixture is reduced, a net change occurs in the direction that produces fewer moles of gas. When volume is increased the change occurs in the direction that produces more moles of gas. Temperature Changes To understand how temperature changes affect equilibrium conditions, the sign of the reaction enthalpy must be known. Assume that the forward reaction is exothermic (heat is evolved): In this reaction, 250 kJ is evolved (indicated by the negative sign) when 1 mole of A reacts completely with 2 moles of B. For reversible reactions, the enthalpy value is always given as if the reaction was one-way in the forward direction. The back reaction (the conversion of C and D into A and B) would be endothermic, absorbing the same amount of heat. The main effect of temperature on equilibrium is in changing the value of the equilibrium constant. Increasing the temperature If the temperature is increased, then the position of equilibrium will move so that the temperature is reduced again. Suppose the system is in equilibrium at 300°C, and the temperature is increased 500°C. To cool down, it needs to absorb the extra heat added. In the case, the back reaction is that in which heat is absorbed. The position of equilibrium therefore moves to the left. The new equilibrium mixture contains more A and B, and less C and D. If the goal is to maximize the amounts of C and D formed, increasing the temperature on a reversible reaction in which the forward reaction is exothermic is a poor approach. Decreasing the temperature? The equilibrium will move in such a way that the temperature increases again. Suppose the system is in equilibrium at 500°C and the temperature is reduced to 400°C. The reaction will tend to heat itself up again to return to the original temperature by favoring the exothermic reaction. The position of equilibrium will move to the right with more A and B converted into C and D at the lower temperature: Consider the formation of water O2+2H2⇌2H2OΔH=−125.7kJ 1. What side of the reaction is favored? Because the heat is a product of the reaction, the reactants are favored. 2. Would the conversion of O2 and H2 to H2O be favored with heat as a product or as a reactant? Heat as a product would shift the reaction forward, creating H2O. The more heat added to the reaction, the more H2O created Summary of Temperature Effects  Increasing the temperature of a system in dynamic equilibrium favors the endothermic reaction. The system counteracts the change by absorbing the extra heat.  Decreasing the temperature of a system in dynamic equilibrium favors the exothermic reaction. The system counteracts the change by producing more heat. Catalysts Adding a catalyst makes absolutely no difference to the position of equilibrium, and Le Châtelier's principle does not apply. This is because a catalyst speeds up the forward and back reaction to the same extent and adding a catalyst does not affect the relative rates of the two reactions, it cannot affect the position of equilibrium. However, catalysts have some application to equilibrium systems. For a dynamic equilibrium to be set up, the rates of the forward reaction and the back reaction must be equal. This does not happen instantly and for very slow reactions, it may take years! A catalyst speeds up the rate at which a reaction reaches dynamic equilibrium.